Question

the ratio of the heights with two similar prisms is 2:7 the surface area of the smaller prism is 50 swuare meters. find the surface area of the larger prism

Answer 1

Answer:

The surface area of the larger prism is 612.5 square meters.

Step-by-step explanation:

If the two prisms are similar, then any length of the both must have the same relationship for the heights. Dimensionally speaking, we have the following expression for the surface area of the prism:

$A_{s} = 2\cdot (w\cdot l + w\cdot h + h \cdot l)$ (1)

Where:

$A_{s}$ - Surface area, in square meters.

$w$ - Width, in meters.

$h$ - Height, in meters.

$l$ - Length, in meters.

If we know that $\frac{l_{B}}{l_{A}} = \frac{7}{2}$, $\frac{w_{B}}{w_{A}} = \frac{7}{2}$ and $\frac{h_{B}}{h_{A}} = \frac{7}{2}$, then we get the following relationship for the volumes of the prisms:

$A_{s, B} = \frac{7^{2}}{2^{2}}\cdot A_{s,A}$ (2)

Where:

$A_{s,A}$ - Surface area of the smaller prism, in square meters.

$A_{s,B}$ - Surface area of the greater prism, in square meters.

If we know that $A_{s,A} = 50\,m^{2}$, then the surface area of the greater prism is:

$A_{s, B} = \frac{7^{2}}{2^{2}}\cdot A_{s,A}$

$A_{s,B} = \frac{7^{2}}{2^{2}}\cdot (50\,cm^{2})$

$A_{s,B} = 612.5\,cm^{2}$

The surface area of the larger prism is 612.5 square meters.